Solidify modifier gap
Just as I said in the comments, it's happening because you you used two separate mesh (two cylinders) which's vertices were so close that you wont notice that there are two vertices. Solidify modifier does something similar to extruding and scaling inwards.
Its just an easy process. I will walk you through it-
First of all apply the object's scale with CTRL+A &gt; scale (or else it will create uneven solidification).
Then go to Edit Mode and box select the vertices as shown and merge them with Alt+M &gt; Merge at center.  (Just  M  in Blender 2.83 and above)

Notice how the gap gets filled...